1. Golf Scores

Yesterday my buddy and I both shot 84, 12 over par. But although we had the same gross scores we noticed that we did not tie any single hole.

Hole Me Him
1 0 2
2 1 0
3 -1 2
4 1 0
5 1 0
6 0 1
7 0 1
8 0 3
9 2 -1
10 3 1
11 1 0
12 0 1
13 2 -1
14 0 1
15 0 1
16 1 0
17 0 2
18 1 -1
Total 12 12

No ties at all seemed very unlikely. What is the probability of that? I tried to estimate it using a Monte Carlo approach with Excel. I got started by simulating just 10 rounds. Tied holes for the 10 simulated rounds were 4,5,2,5,3,8,5,8,2,6. The results indeed suggest that the probability of no ties is quite low. But how low?

I would be interested in a formulaic solution to this problem. For simplicity, assume that each player always has the same set of hole by hole scores, totaling 12 over par, but that the hole by hole pattern of the scores can vary.

Thanks,
Jonart

2. Re: Golf Scores

Hi Jonart
you may find the solution here ... cool article on match play
http://toddwschneider.com/posts/how-...tch-play-golf/

3. Re: Golf Scores

In general it would also be interesting to see if certain holes with comparable traits (short, hills, hazards) resulted in similar within player scores.

4. Re: Golf Scores

Jonart, I took the approach of using a Poisson PMF on a per-hole basis
where lamda is the average # of strokes. I squared each p(x) to find the
probability for two matched players, and summed the results of x = 1, 2, 3, ...
on up to 30. Here's the results:

lambda ---p of tie
2 ------- 0.188
3 ------- 0.164
4 ------- 0.143
5 -------0.127
6 -------0.116
7 -------0.107

I dunno if this method is correct but it at least gives believable results

Art

5. Re: Golf Scores

http://jsmith.co/sites/default/files/Paperima.pdf
Probabilities of ties in match play between top notch pros is very high...
about 0.4 for par 5, 0.47 for par 4 and 0.5 to 0.56 for par 3.

Art

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